Maybe the recording I'm thinking of is earlier than this (although, qualifier, it may not have been a "Presidential" speech, possibly a Congressional one?). Does it start with morning music (something like "Breakfast Serenade") and eventually include coverage of a baseball game (I'm not in a position to listen to the NPR link and my casette binder - it was something like 12/18 tapes - have been packed away for years)?
EDIT - okay, it sounds like same thing:
"From Thursday, September 21, 1939. President Franklin Roosevelt gave a speech to Congress this day, and station WJSV, 1460 AM in Washington, DC decided to preserve the entire day's broadcast, from sign-on at 6 a.m. to sign-off at 1:00 a.m. the following morning, to commemorate it. To see a complete, hour-by-hour program schedule"
Roosevelt gave his speech at 2:00 in the afternoon and the baseball game is at about 11:30 am. Funny, NPR says the National Archive ordered the recording, this capsule says WJSV decided to do it, and the story, as I heard it in the late 80's, was that it was a happy accident involving an order to record the speech, a new employee and a stack of transcription discs (he assumed they did this every day, whereas transcription discs were generally too pricey for that).